SUPPLEMENTARY INFORMATIONArticles https://doi.org/10.1038/s41563-018-0023-7
In the format provided by the authors and unedited.
Acoustically modulated magnetic resonance imaging of gas-filled protein nanostructures
George J. Lu 1, Arash Farhadi 2, Jerzy O. Szablowski1, Audrey Lee-Gosselin1, Samuel R. Barnes 3, Anupama Lakshmanan2, Raymond W. Bourdeau 1 and Mikhail G. Shapiro 1*
1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, USA. 2Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA. 3Department of Radiology, Loma Linda University, Loma Linda, CA, USA. *e-mail: [email protected]
Nature Materials | www.nature.com/naturematerials © 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. Acoustically modulated magnetic resonance imaging of gas-filled protein nanostructures
George J. Lu1, Arash Farhadi2, Jerzy O. Szablowski1, Audrey Lee-Gosselin1, Samuel R. Barnes3, Anupama Lakshmanan2, Raymond W. Bourdeau1, Mikhail G. Shapiro1*
1Division of Chemistry and Chemical Engineering, 2Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA. 3Department of Radiology, Loma Linda University, Loma Linda, CA.
* Correspondence should be addressed to M.G.S. ([email protected])
Supplementary Information
Theoretical consideration of the T2/T2* relaxation produced by gas vesicles Relaxation theory1-7 describes the T2/T2* relaxation of water near a contrast agent in three primary regimes: (1) the motional averaging regime, where �� ∙ � ≪ 1; (2) the static dephasing regime, where �� ∙ � ≫ 1; and (3) the intermediate regime, where �� ∙ � ~ 1. Here Δωr is the root-mean-square frequency shift at the surface of the contrast agent and τD is the time for a water molecule to diffuse across the distance of the contrast agent’s radius. Considering a single gas vesicle (GV) at high field (Fig. 1b), we obtain �� ≈ �� ∙ �� ≈ 10 �� and � ≈ 10 ���; therefore T2/T2* relaxation on the nanoscale (e.g., everywhere inside an agarose well containing GVs) occurs in the motional averaging regime. At the same time, the macroscale ΔB field around a millimetre-sized agarose well containing GVs (at a volume fraction of ~ 0.01%) (Fig. 1d) has a predicted �� ≈ 10 �� and � ≈ 10 ���, resulting in T2/T2* relaxation in the static dephasing regime. These relaxation regimes are manifest in the T2-weighted and T2*-weighted images shown in Supplementary Fig. 1. The spin relaxation at the centre of the well is predominantly a result of the nanoscale ΔB field, while the spin relaxation near the rim of the wells results from the macroscale ΔB field. The rim usually appears darker than the centre of the well in T2*-weighted images because of the more efficient relaxation of water 1H in the static dephasing regime than in the motional averaging regime. On the other hand, the rim of the wells lacks hypointense contrast in T2-weighted images, since π pulses can effectively refocus the dephasing of 1H spins in the static dephasing regime. Relaxation theory also sheds light on the behaviour of clustered GVs. The micron-size GV clusters are